Transform Theory - Study Mode
[#6] Given the Fourier series in (-π, π) for f(x) = x cosx, the value of a 0 will be
Correct Answer
(B) 0
[#7] Laplace transform of the function f(t) is given by $${ ext{F}}left( { ext{s}}
ight) = { ext{L}}left{ {{ ext{f}}left( { ext{t}}
ight)}
ight} = int_0^infty {{ ext{f}}left( { ext{t}}
ight){{ ext{e}}^{ - { ext{st}}}}{ ext{dt}}{ ext{.}}} $$ xa0 xa0 xa0 Laplace transform of the function shown below is given by
Correct Answer
(C) $$frac{{2 - 2{{ ext{e}}^{ - { ext{s}}}}}}{{ ext{s}}}$$
[#8] If L defines the Laplace Transform of a function, L [sin (at)] will be equal to
Correct Answer
(B) $$frac{{ ext{a}}}{{{{ ext{s}}^2} + {{ ext{a}}^2}}}$$
[#9] The Fourier series expansion of the saw-toothed waveform f(x) = x in (-π, π) of period 2π gives the series, $$1 - frac{1}{3} + frac{1}{5} - frac{1}{7} + ,....$$ The sum is equal to
Correct Answer
(D) $$frac{pi }{4}$$
[#10] Laplace transform of 8t 3
Correct Answer
(D) $$frac{{48}}{{{{ ext{S}}^4}}}$$